Prime p₀= 425576370416470307 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 10 2 118 2 16 2 28 2 (?)
a_n: 0 2 60 62 72 74 192 194 210 212 240 242
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 242
Found by: Cruncher Pete
db: batch=70, k=12, 58 10 118 16 28

SPT(14)	425576288722365353	0 14 18 60 84 110 128 180 198 224 248 290 294 308	-81694104954
SPT(14)	425576298484895741	0 56 66 72 86 122 138 140 156 192 206 212 222 278	-71931574566
TPT(12)	425576310399240041	0 2 18 20 108 110 138 140 150 152 240 242	-60017230266
SPT(14)	425576323455143999	0 8 12 20 42 54 74 78 98 110 132 140 144 152	-46961326308
SPT(14)	425576349427090633	0 10 30 36 66 78 100 114 136 148 178 184 204 214	-20989379674
SPT(14)	425576356349655397	0 46 52 60 82 102 106 150 154 174 196 204 210 256	-14066814910
SPT(14)	425576371352219293	0 6 94 126 136 216 238 426 448 528 538 570 658 664	935748986
SPT(16)	425576384534689627	0 16 46 82 114 130 142 154 252 264 276 292 324 360 390 406	14118219320
SPT(14)	425576389828393649	0 32 42 48 72 98 104 108 114 140 164 170 180 212	19411923342
SPT(14)	425576409845808527	0 12 42 50 120 132 144 182 194 206 276 284 314 326	39429338220
TPT(12)	425576430117754931	0 2 66 68 78 80 96 98 108 110 168 170	59701284624